Crash and Smash
Classical Mechanics
Level
2
Take two random particles of arbitrary masses. Now suppose these particles travel at different constant velocities and they come into an elastic collision, will they ever have the same instantaneous velocity (the same velocity at an instant)?
Yes, but only if both particles have the same mass
No
Yes, but only if it is a perfectly inelastic collision
Yes
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Both particles will have the same speed at some point or for multiple points depending on the type of collision. If it is an inelastic collision, both particles will have the same velocity (includes direction) throughout the entire trip after the collision assuming there are no external forces to disturb this situation.
However, for a perfectly inelastic collision, it does not matter what masses these particles have but they will have the same velocity for at least one moment in time. it is best to visualize this with some depiction such as a velocity-time graph. As can be seen below, the particles will arrive at a common position and there will be equal and opposite forces acting on each other. This means both particles will have to decelerate and then accelerate again after some time. During the time interval in which they accelerate they will meet at a common velocity for just that one instant and then go on with their own motion. This is of course not including the fact that they have the same velocities when at rest.